Magnetic Resonance Imaging (MRI) is notoriously slow. Clinical exams typically take on the order of 1 hour per patient. This severely limits throughput, makes costs high, and decreases the availability of MRI to a broader community. Various efforts have been made in an attempt to increase the speed of image acquisition as increases by even a factor of two could have a significant impact on the cost of health care and open up new applications for MRI.
MRI is a medical imaging technique based on the phenomenon of nuclear magnetic resonance (NMR). In contrast with medical imaging techniques using X-rays, MRI is capable of producing high resolution images for a variety of applications and anatomies without using ionizing radiation. Typically, an MRI scan is initiated by generating a strong magnetic field which Typically, an MRI scan is initiated by generating a strong magnetic field which aligns the magnetic moments of protons (i.e., the nuclei of hydrogen atoms) in the volume of interest (for example, a patient) being scanned. A radiofrequency (RF) pulse is then transmitted into the volume of interest. If the frequency of the RF pulse matches the Larmor frequency of protons in the volume, the pulse may induce a spin-flip transition of the protons from an aligned state to a higher-energy anti-aligned state. When the protons relax after the pulse, they will then emit RF signals at the Larmor frequency which can be detected with receiver coils. The intensity of the detected signal is representative of the concentration of protons in the volume.
The Larmor frequency of a proton is proportional to the strength of the magnetic field. Consequently, if the applied magnetic field is generated with a known spatial gradient, then the Larmor frequency of protons will also have a known spatial localization. Because the frequencies of the detected RF signals from the relaxing protons are known (i.e., the signal data is measured in the frequency domain, or k-space), and because these frequencies are correlated with spatial locations through the known magnetic gradient field, the signal can be transformed from the frequency domain to the spatial domain to produce an image. Because the gradient field provides the correlation between the frequency domain and spatial (or image) domain, it is sometimes called an encoding field.
Conventionally, several orthogonal linear gradients are used in MRI, and several repetition times (TRs) are needed to gather sufficient information to reconstruct an image of the volume. Thus, conventional MRI requires relatively long scan times. For an N×N image, a classic fully-sampled linear gradient data collection scheme requires N repetitions of the basic procedure to generate N lines of k-space (that is, the 2D or 3D Fourier transform of the magnetic resonance image measured). During each repetition time, linear magnetic gradients create plane-wave oscillations in the phase across the image. As the phase variation replicates the kernel of the Fourier transform, the k-space data set is reconstructed via the fast Fourier transform (FFT). When k-space lines are undersampled, aliasing occurs as image fold over.
Researchers have developed various techniques in attempts to reduce scan times. For example, one recent advance in MRI, known as parallel imaging, involves acquiring signals simultaneously with multiple receiver coils. The acquired data can be under-sampled and the resulting aliasing can be unwrapped using receiver coil sensitivity information to produce full images. Parallel imaging methods generally combine spatially-weighted data from multiple simultaneous measurements in order to reduce scan time. Most parallel imaging approaches collect a reduced data set for later interpolation for a Fourier or algebraic reconstruction. By relying on the Fourier reconstruction approach, conventional approaches use orthogonal gradients that complement each other. These gradients, however, can be inefficient with regard to information gathered from the coil sensitivities, resulting in longer scan times and/or reduced image resolution.
Parallel reconstruction conventionally operates on an undersampled frequency domain data set, and data sets from separate coils are either combined in the k-space domain, in the image domain, or a hybrid space. GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisition), SENSE (Sensitivity Encoding), and SMASH (SiMultaneous Acquisition of Spatial Harmonics) exemplify three known approaches within a Fourier acquisition scheme using linear magnetic gradients for signal encoding. SMASH uses linear combinations of coil sensitivity profiles as a free parameter to shift existing k-space lines to fit omitted data. In order to shift k-space lines, linear combinations of coil profiles must approximate spatially oscillating functions. In practice, coil sensitivity profiles are slowly varying and spatially distinct. The limited flexibility in changing coil profiles makes implementation on an anatomy-constrained geometry difficult.
Parallel imaging, the use of locally sensitive receivers to provide encoding, typically aims to reduce scan time by reconstructing images from a reduced number of timepoints. Sodickson D K, Manning W J (1997) Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magnetic Resonance in Medicine 38: 591-603; Jakob P M, Grisowld M A, Edelman R R, Sodickson D K (1998) AUTO-SMASH: a self-calibrating technique for SMASH imaging. Magnetic Resonance Materials in Physics, Biology and Medicine 7: 42-54; Bydder M, Larkman D J, Hajnal J V (2002) Generalized SMASH imaging. Magnetic Resonance in Medicine 47: 160-170; Griswold M A, Jakob P M, Heidemann R M, Nittka M, Jellus V, et al. (2002) Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 47: 1202-1210; Blaimer M, Breuer F, Mueller M, Heidemann R M, Griswold M A, et al. (2004) SMASH, SENSE, PILS, GRAPPA: how to choose the optimal method. 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To facilitate this, several groups, including the inventors of the present invention, have studied whether the geometry of gradient encoding can better complement the information from locally sensitive receivers. Stockmann J P, Ciris P A, Galiana G, Tam L, Constable R T, O-space imaging: Highly efficient parallel imaging using second-order nonlinear fields as encoding gradients with no phase encoding, Magn. Reson. Med., 64(2): 447-456, 2010. Stockmann J P, Galiana G, Tam L K, Nixon T W, Constable R T (2011) First O-Space images using a high-power, actively-shielded 12-cm Z2 gradient insert on a human 3T scanner. Proceedings of the ISMRM 19th Annual Meeting: 717; Stockmann J P G, G., Tam L, Juchem C, Nixon T W, Constable R T (2013) In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration. Magn Reson Med 69: 444-455; Tam L K, Stockmann J P, Galiana G, Constable R T (2011) Null Space Imaging: Nonlinear Magnetic Encoding Fields Designed Complementary to Receiver Coil Sensitivities for Improved Acceleration in Parallel Imaging. Magnetic Resonance in Medicine 68(4): 1166-75; Gallichan D, Cocosco C, Dewdney A, Schultz G, Welz A, et al. (2011) Simultaneously driven linear and nonlinear spatial encoding fields in MRI. Magnetic Resonance in Medicine 65: 702-714; Schultz G, Weber H, Gallichan D, Witschey W R, Welz A M, et al. (2011) Radial Imaging with Multipolar Magnetic Encoding Fields. IEEE Trans Med Imag 16: 17; Hennig J, Welz A M, Schultz G, Korvink J, Liu Z, et al. (2008) Parallel imaging in non-bijective, curvilinear magnetic field gradients: a concept study. Magnetic Resonance Materials in Physics, Biology and Medicine 21: 5-14. The previous work of the inventors has examined whether this allows a further reduction in the minimum number of echoes due to increased encoding efficiency when the encoding is shared between the magnetic field gradients and the receiver coil sensitivity profiles. This has led to many studies of image encoding with nonlinear gradient shapes, producing good image reconstructions from highly undersampled datasets. Stockmann J P, Ciris P A, Galiana G, Tam L, Constable R T, O-space imaging: Highly efficient parallel imaging using second-order nonlinear fields as encoding gradients with no phase encoding, Magn. Reson. Med., 64(2): 447-456, 2010. Stockmann J P, Galiana G, Tam L K, Nixon T W, Constable R T (2011) First O-Space images using a high-power, actively-shielded 12-cm Z2 gradient insert on a human 3T scanner. Proceedings of the ISMRM 19th Annual Meeting: 717; Stockmann J P G, G., Tam L, Juchem C, Nixon T W, Constable R T (2013) In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration. Magn Reson Med 69: 444-455; Tam L K, Stockmann J P, Galiana G, Constable R T (2011) Null Space Imaging: Nonlinear Magnetic Encoding Fields Designed Complementary to Receiver Coil Sensitivities for Improved Acceleration in Parallel Imaging. Magnetic Resonance in Medicine 68(4): 1166-75. Previous nonlinear gradient encoding work has also explored single shot trajectories employing EPI (Echo Planar Image)-like readouts. One example is 4D-RIO (4-Dimensional Radial In/Out) which uses an offset radial acquisitions on both linear and nonlinear gradient channels. Layton K J, Gallichan D, Testud F, Cocosco C A, Welz A M, et al. (2012) Single shot trajectory design for region-specific imaging using linear and nonlinear magnetic encoding fields. Magn Reson Med. EPI-like readouts have also been combined with trajectories designed to enhance or sacrifice resolution in different parts of the field of view. Gallichan D, Testud F, Barmet C, Cocosco C, Welz A, et al. (2012) Simultaneous Linear and Nonlinear Encoding in a Single Shot; Proceedings of the 20th ISMRM: 292.
In another approach to reducing scan time, some research has aimed to modify receiver coils, allowing for less data collection and better unwrapping of the aliasing artifacts. This research has focused on increasing the number of receiver coils to localize the sensitivity, only to face issues of ballooning cost and diminishing returns. Recent hardware advances used up to 96 receiver coil elements. Hardware costs increase dramatically with the number of coils since each coil must use a separate receiver, cabling, pre-amplifier, and so on. The difficulty of constructing large coil arrays is nontrivial as elements must be de-coupled. Nearest neighbor approaches through overlapping coils and pre-amplifier decoupling partially addresses inductive coupling of numerous further elements. Increasing coil number reduces the g-factor, a pixel by pixel measure of noise amplification, but drives the cost much higher and exacerbates the decoupling problem. Moving to higher fields and including spatially selective parallel transmission pulses show promise, but fundamentally does not address the underlying encoding problem.
Improvements have been made in SENSE and GRAPPA reconstructions to preserve reconstruction quality, but these penalize acceleration in image acquisition. There has been a trend towards auto-calibration, which has been adopted by SENSE/SMASH as generalized SENSE/SMASH (GSENSE/GSMASH). Another generalization is the expansion of data sampling trajectories to radial and spiral k-space trajectories. For example in radial k-space sampling, an auto-calibration scan (ACS) is collected near the center of k-space during each readout. Using auto-calibration improves image quality at the expense of imaging time by requiring more data collected, or introduces bias by emphasizing low spatial frequency components of the image.
Though sharing a frequency and phase acquisition scheme with Cartesian data, PatLoc (parallel imaging technique with local gradients) performs orthogonal gradient imaging with nonlinear gradients. Non-bijective curvilinear gradients enable faster gradient switching through dB/dt reduction. PatLoc reconstruction relies on the local orthogonality in the magnetic fields to apply a volumetric correction term to the integrand of the signal integral. With the volumetric correction, the image is reconstructed using a fast Fourier transform (FFT). Limiting gradients to a pair-wise orthogonal multi-polar gradient set causes position dependent resolution, with a noticeable absence of signal localization in the center of the image. To date, higher-order gradient encoding has only been performed using custom-built gradient coils.